Holomorphic Interpolation Schemes for Multimodal Manifold Learning
In recent years, multimodal data, e.g., data acquired by different sensors, have become abundant, raising many new challenges for data analysis. One particular task of interest concerns multimodal data representation, and particularly, how to construct an informative representation that reveals the mutual and unique features of the modalities. This task has drawn much attention and has been addressed using different approaches. In this talk, I will present an approach based on manifold learning and kernel methods. Specifically, following a recent line of work that relies on various kernel combinations, a new framework for kernel interpolation will be presented. While the framework and analysis tools are general, the focus is on a particular interpolation scheme that is capable to identify and extract mutual and unique spectral components. Based on complex analysis, I will show the analysis of this interpolation scheme that includes two theoretical results. First, I will present a guarantee for the existence of a mutual eigenvector, if the interpolation scheme exhibits a particular log-linear structure. This property is important for visualization and extraction of mutual components. Second, I will present a bound on the eigenvectors correlation, that quantifies the eigenvectors’ degree of commonality. Our approach and analysis will be demonstrated on several numerical examples.
MSc. student under the supervision of Professor Ronen Talmon.